# Continuity of a multivariable function

1. Oct 23, 2012

### Jalo

1. The problem statement, all variables and given/known data

Given the function:

x*y / (4-x²-2y²) if x²+2y² ≠4
0 if x²+2y² = 4

Check if the function is continuous.

2. Relevant equations

3. The attempt at a solution

I tried using various ways to see if the result of the limit as (x,y)→(2,0) was the same, such as y=x-2, y=(x-2)², etc..
I didn't manage to prove that the limit didn't existed. I always arrive at the 0/0 indetermination...

If anyone could point me in the right direction I'd appreciate!

D.

2. Oct 23, 2012

### hedipaldi

convert to ellyptic coordinates x=2rcos(t); y=sqt(2)rsin(t) and compute the limit as r tends to 0,using L'hopital's rule.If the limit is not identically 0 (or depends on t),then the function is not continuous at the poins on the ellipse.

3. Oct 23, 2012

### Jalo

Hmm I'll try doing it. However I never learned ellyptic coordinates. I'm wondering if there's any other way to solve this!

Last edited: Oct 23, 2012
4. Oct 23, 2012

### hedipaldi

o.k don't name it,just substitute in the function and compute the limit as r tends to 1 and t is constant.